This invention relates generally to proportional-integral control systems and methods, and more particularly to proportional-integral control methods in a mass flow controller.
Many manufacturing processes require that the introduction rates of process gases into a process chamber be strictly controlled. These types of processes may use mass flow controllers (MFC) to control the flow rate of gases. A mass flow controller is a closed loop device that sets, measures, and controls the flow of the mass of a process gas into a process chamber. Semiconductor applications have been and continue to be the driving force behind product development in mass flow controller technology. Nonetheless, mass flow control is useful in other industries, such as the pharmaceutical industry and the food industry.
A thermal mass flow controller is composed of a front half which includes a flow sensor and a back half which includes a control valve. The flow sensor is often composed of twin resistance temperature sensors wound around a capillary tube. When gas flows through the sensor, heat is carried downstream and the temperature difference is proportional to the mass flow rate of the gas. The temperature difference will cause differential resistance changes in the sensor elements. The control valve receives a signal via electronics from the flow sensor to regulate gas flow. Solenoid activated valves are often used as control valves because of their simplicity, quick response, robustness, and low cost.
Traditional feedback control methods are often used to control the flow of gas in a mass flow controller. In a mass flow controller, the system includes a set-point representing the desired flow of gas in the mass flow controller, a sensor which senses the actual flow rate of a gas in the mass flow controller, a controller, and a plant. The controller consists of electronic circuitry which controls the action of the plant. In the case of the mass flow controller, the plant may be a solenoid activated valve which directly controls the actual flow rate of a gas into a process chamber. The electronic circuitry in the controller can generate a control signal (valve drive signal) based on an error signal. The error signal is the difference between the set-point signal and a feedback signal. In the case of a mass flow controller, the set-point signal is a function of the desired flow rate and the feedback signal is a function of actual flow rate.
Feedback control modes often employed are proportional control, integral control, and derivative control. With proportional control, the control signal is proportional to an error signal. The controller gain can be adjusted to make the control signal sensitive to small deviations between the set-point signal and the feedback signal. Design of the controller gain can also be chosen to make the control signal increase or decrease as the deviation between the set-point signal as the feedback signal increases or decreases. An inherent drawback of proportional-only control is that it is unable to eliminate steady-state errors.
Integral control is often widely used because it provides the advantage of elimination of errors. With integral control, the control signal depends on the integral of the error signal over time. During steady-state operation of the system, if the control error is constant, the integral of the error will change with time and produce an action in the plant that ultimately causes the error to go to zero. The integral controller is not often used alone since little control action in the plant occurs until the error signal has persisted for some time. Proportional control, however, immediately amplifies the error signal. Therefore, integral control is often used in conjunction with proportional control in what is called a proportional integral (PI) controller to generate the valve drive signal (control signal).
Derivative control functions to anticipate the behavior of the error signal. With derivative control, the control signal depends on the rate of change of the error signal. Derivative control also tends to reduce the time needed for the process to reach steady state. Derivative control is used in conjunction with either proportional control or proportional-integral control.
A persistent problem with typical mass flow controllers is that the solenoid valve action is not a linear function of the valve drive signal (control signal). The relationship between the valve drive signal and the actual flow through the mass flow controller for the solenoid valve is with hysterisis. FIG. 1 is a graphical representation of the valve drive signal versus actual flow through a mass flow controller. The gain of the valve increases with flow. The valve drive signal is graphed along the x-axis and the actual flow through the mass flow controller is graphed along y-axis. As the valve drive signal increases, the actual flow through the mass flow controller does not begin to increase until the valve drive signal reaches a value of X3. This amount of time it takes the valve drive signal to reach X3 is denoted as the dead time. Once the valve drive signal reaches the value of X3, the actual flow begins to increase in a proportional (but non-linear) manner as a function of the valve drive signal. Once the valve drive signal has reached a maximum value of X4, decreasing the valve drive signal does not immediately cause a decrease in the actual flow through the mass flow controller. The valve drive signal must be decreased to a level of X2 until the actual flow begins to decrease in a proportional (but non-linear) manner as a function of the valve drive signal. Once the valve drive signal reaches the level of X1, the actual flow may cease. It can be seen from FIG. 1 that when the valve drive signal is weak the response of the valve is negligible, yet when the valve drive signal passes a certain xe2x80x9cthresholdxe2x80x9d (X3) the valve response is greatly increased. The gain of the valve increases with flow. This type of non-linear characteristics associated with the solenoid valve is extremely difficult to control and cannot be fully compensated.
Ultimately, there is a need to compensate for the non-linear behavior of actual flow in a mass flow controller caused by the non-linear relationship between the valve drive signal and the actual flow through the solenoid activated valves.
The present invention provides a system and method for generating a valve drive signal that substantially eliminates or reduces disadvantages and problems associated with previously developed systems and methods for generating a valve drive signal.
More specifically the present invention provides a system and method for generating a valve drive signal using a variable PI controller in a mass flow controller. The method includes multiplying an error signal with a proportional gain factor to generate a proportional signal. The method also includes implementing an integral function on the error signal. The integral function includes an integral gain factor which functions as the variable gain in the PI controller. For set-point signals less than a normalized predetermined percentage p of the maximum set-point, the integral gain factor is equal to       [                            (                                    1              p                        -                          max              ⁡                              (                x                )                                              )                ⁢        A            +      B        ]    ,
where A is a first gain constant, B is a second gain constant, and max(x) is the maximum value of the normalized set-point signal. Otherwise, the integral gain factor is equal to       [                            (                                    1              x                        -                          max              ⁡                              (                x                )                                              )                ⁢        A            +      B        ]    ,
where A is the first gain constant, B is the second gain constant, and x is the normalized set-point signal. Implementing the integral function produces an integral signal. Lastly, the integral signal and the proportional signal are summed to generate the value drive signal. The error signal is a function of the difference between a set-point signal and a feedback signal. The set-point signal is a function of a desired flow rate in the mass flow controller, while the feedback signal is a function of the actual flow rate through the mass flow controller.
The present invention provides an important technical advantage in that it enables the integral gain factor in the PI controller to be a variable gain. The integral gain factor is a function of the set-point signal. Thus, for a low set-point signal the effect of the lower valve gain can be compensated with higher integral gain. This mechanism maintains the same control system feedback loop gain regardless of the operating point and enables the system response to be rendered uniform in speed of response and disturbance rejection characteristic, effectively concealing delayed step response and sluggish recovery from inlet pressure disturbance while operating at low set-point (or operating point).
Another technical advantage of the present invention is that it reduces the dead time associated with the valve in the mass flow controller, allowing the control signal to ramp up through the valve dead time with the same efficiency whether the mass flow controller is ramping to 100% of the maximum flow or 5% of the maximum flow.